Anyone doing contracts, requirements documents, writing/editing cycles could use something like this with varying additional capabilities.

With no change to philosophy (still staying on the user side), a system could be made based off the principles of existing software.

You need some workflow management software + a document store. The document store needs to provide rich text editing, and the ability to edit only specific sections in parallel. "section" is a customizable unit depending on the type of contract. Could be paragraphs, or larger logical units. Part of the workflow management is kicking the contract back and forth between you and your collaborators and the other stakeholders. At various stages it's editable by different people, some stages are just for review (not edit), finally various sign-off stages.

It's pretty typical of requirements document databases. You'd need it exposable to third parties outside your company, and you'd also need confidence in privacy and security. Neither are trivial, but neither are impossible.

The software for your needs literally exists, but isn't marketed to you. It's too costly for smaller offices (both licensing costs and management costs), and would require a good sales pitch because, well, people don't like change.